A352847 Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph.

0, 0, 48, 576, 3840, 19200, 80640, 301056, 1032192, 3317760, 10137600, 29736960, 84344832, 232587264, 626196480, 1651507200, 4278190080, 10909384704, 27433893888, 68136468480, 167352729600, 406931374080, 980510834688, 2343038877696, 5556613939200

Offset: 1

Author

Ben Eck, Apr 05 2022

Keywords

• nonn
• easy

Comments

The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Crossrefs

Cf. A129002.

Programs

Mathematica

a[n_] := (2^n)*Binomial[n,2]*(n-1)*(n-2); Array[a, 25] (* Amiram Eldar, Apr 22 2022 *)

Python

from math import comb
def a(n):
    return (2**n)*comb(n,2)*(n-2)*(n-1)

Formula

a(n) = 2^n*binomial(n,2)*(n-1)*(n-2).

G.f.: 48*x^3*(1 + 2*x)/(1 - 2*x)^5. - Stefano Spezia, Apr 15 2022

Sum_{n>=3} 1/a(n) = 9/8 + log(2)^2/2 - 3*log(2)/4 - Pi^2/12. - Amiram Eldar, Apr 22 2022